Habash al-Hasib al-Marwazi

Abu Jafar Ahmad ibn Abdallah al-Marwazi, known as Habash al-Hasib, was born around 770 (766 in some sources) in or near Merv in Khorasan, now the area around the town of Mary in Turkmenistan. Little is known of his life. “Habash” means “Abyssinian” and was probably a nickname given for his dark complexion; “al-Hasib” means “the calculator”, that is, a mathematical astronomer.

He spent most of his life in Baghdad, living through the reigns of the Abbasid caliphs al-Ma’mun and al-Mu’tasim, which is why he is also called al-Baghdadi. Sources place him in the Baghdad scientific circle around al-Ma’mun, but it is not certain whether he formally belonged to the caliph’s group of observers or merely followed their work closely. According to Ibn Yunus he observed in Baghdad for about thirty-five years; the earliest recorded observations date from 829.

Three astronomical tables (zijes) are ascribed to him. The first followed the Indian tradition, based on Brahmagupta’s Siddhanta; the next, and best known, “Al-Zij al-Mumtahan” (“The Tested Zij”), rests on observations and is arranged on the Ptolemaic model. A third, the “Small Zij” or “Zij al-Shah”, has not survived. A table known as the “Damascene Zij” is also associated with his name.

His most notable achievement lay in applying trigonometry to problems of spherical astronomy. Following al-Khwarizmi he compiled sine tables, clearly distinguished the “reversed sine” (versine) from the sine, and was among the first to compile tables of the “shadow” (zill), that is, the tangent; he is also counted among those who introduced the cotangent. He proposed a way of finding the time from the Sun’s altitude that later astronomers used. His iterative method for the parallax problem has since been compared with Kepler’s equation.

Habash wrote on the sphere and its use, the spherical astrolabe, the armillary sphere (“dhat al-halaq”) and sundials, as well as a book on the distances and sizes of the celestial bodies. His son Abu Jafar was also an astronomer and instrument maker. Habash lived to be over a hundred; his death is placed between 864 and 874, probably at Samarra, and after 869.

His work influenced later scholars: Abu Nasr ibn Iraq wrote a treatise on his zij, and al-Biruni, calling him a “sage”, cited “The Tested Zij” repeatedly and devoted a separate supplement to it.